1. Field of the Invention
The present invention relates to a wire cut-type electric discharging method employable for creating a tapered surface on a work by employing a wire serving as an electrode held in an inclined state relative to a reference surface of the work.
2. Description of the Prior Art
To facilitate understanding of the present invention, a conventional wire cut-type electric discharge apparatus will be described below with reference to FIGS. 10 to 14.
FIG. 10 is a schematic perspective view of the apparatus in a disassembled state. In the drawing, reference numeral 1 designates a wire serving as an electrode for a cutting operation, reference numeral 2 designates an upper wire guide for guiding the movement of the wire 1, reference numeral 3 designates a driving unit for moving the upper wire guide 2 in a U-direction, reference numeral 4 designates another driving unit for moving the upper wire guide in a V-direction, reference numeral 5 designates a lower wire guide for guiding the movement of the wire 1, reference numeral 6 designates a wire unwinding reel, reference numeral 7 designates a wire feeding roller, reference numeral 8 a wire winding reel, reference numeral 9 designates a wire winding guide roller, reference numeral 10 designates a work held in a space between the upper wire guide 2 and the lower wire guide 5, reference numeral 11 designates a movable table on which the work 10 is firmly mounted, reference numeral 12 designates a driving unit for driving the movable table 11 in an X-coordinate direction and reference numeral 13 designates another driving unit for driving the movable table 11 in a Y-coordinate direction.
FIGS. 11 and 12 illustrate by way of example a work on which taper machining has been carried out by operation of the above-described electric discharge apparatus. FIG. 11 illustrates a case where taper machining has been carried out on a truncated conical work 10 and FIG. 12 illustrates a case where taper machining has been carried out on a work 10 which has the same corner radius on both the upper and lower surfaces thereof. Incidentally, FIG. 11(a) and FIG. 12(a) are plan views of the work 10, FIG. 11(b) and FIG. 12(b) are front views of the work 10 and FIG. 11(c) and FIG. 12(c) are perspective views of the work 10, respectively.
FIG. 13 is a fragmentary sectional view of the work 10 as seen during taper machining. In the drawing, reference character t designates a thickness of the work 10, reference character .theta..sub.i designates an inclination angle of the wire 1 relative to a vertical plane (i.e., a wire inclination angle) and reference character t.sub.i designates a distance of the machining region between the upper surface 10a and the lower surface 10b of the work 10 as seen in the horizontal direction. The distance t.sub.i represents a quantity which is determined by the wire inclination angle .theta..sub.i and the thickness t of the work 10, i.e., the amount of taper-offset.
FIG. 14 is an explanatory plan view illustrating a machining track which is created by a conventional method of performing a taper machining operation on the work 10 having the same corner radius on both its upper and lower surfaces. In the drawing, reference numeral 20 designates a first straight section, reference numeral 21 designates an arc-shaped section extending tangential to the first straight section 20 and reference numeral 22 designates a second straight section extending in a likewise tangential manner to the corner section 21. Reference characters l.sub.1, c.sub.1 and l.sub.2 designate a first straight track, an arc-shaped track and a second straight track on the lower surface 10b of the work 10 and reference characters l.sub.3, c.sub.2 and l.sub.4 designate a first straight track, an arc-shaped track and a second straight track on the upper surface 10a of the work 10. Reference characters O.sub.1 and O.sub.2 designate center points of the arc-shaped tracks c.sub.1 and c.sub.2. Reference character r designates a radius of each of the arc-shaped tracks c.sub.1 and c.sub. 2 on the upper and lower surfaces of the work 10. The radius r of the lower arc-shaped track c.sub.1 is equal to that of the upper arc-shaped track c.sub.2. Reference character t.sub.1 designates an amount of taper-offset at the first straight section 20 and reference character t.sub.2 designates an amount of taper-offset at the second straight section 22. Both the quantities t.sub.1 and t.sub.2 are represented by the following equations. EQU t.sub.1 =t.times.tan .theta..sub.1 EQU t.sub.2 =t.times.tan .theta..sub.2
where t is a thickness of the work and .theta..sub.1 and .theta..sub.2 are wire inclination angels at the first and second straight sections.
Further, reference character g.sub.1 designates a machined groove which appears on the lower surface 10b of the work 10 after the wire 1 has been applied, and reference character g.sub.2 designates another machined groove which appears on the upper surface 10a of the work 10 after the wire 1 has been applied.
Next, the operation of the apparatus will be described below.
As is well known, a wire cut-type electric discharge machining operation is performed such that a work 10 is displaced relative to a wire 1 by actuating driving units 12 and 13 to operate the movable table 11 and a product having a desired contour is cut out from the work 10. In addition to the foregoing electric discharge machining operation, there is a known method of performing a taper machining operation on a work 10 to create a slantwise extending surface by operating the electric discharge apparatus with synchronous cooperation of the driving units 12 and 13 with the driving units 3 and 4 to move the wire guide 2. A hitherto known taper machining method is typically shown in FIGS. 11 and 12. FIG. 11 shows taper machining on a truncated conical product and FIG. 12 shows taper machining similar to that in FIG. 11 with the exception that four arc-shaped sections are taper machined with the same radius. Particularly, the taper machining shown in FIG. 12 should be carried out on the arc-shaped section at the same machining speed on both the upper and lower surfaces of the work 10 by the same amount within the same period of time on both the upper and lower surfaces of the work. This causes the width of the machined groove along the edge line of the upper surface of the work to be equal to that of the lower surface of the same. Therefore, the method shown in FIG. 12 is essential for performing a machining operation to an accurate taper angle.
The method shown in FIG. 12 will be described in more detail below with reference to FIG. 14.
As disclosed in Japanese Patent Publication No. 49053/1986, to create an arc-shaped contour on an upper surface 10a of a work 10 corresponding to an arc-shaped section 21 having first and second straight sections 20 and 22 extended therefrom on a lower surface 10b of the work 10, first and second straight tracks l.sub.3 and l.sub.4 on the upper surface 10a of the work 10 spaced away from first and second straight tracks l.sub.1 and l.sub.2 on the lower surface 10b of the work 10 by taper-offset quantities t.sub.1 and t.sub.2 are first derived and an arc-shaped track c.sub.2 extending tangential to the first and second straight tracks l.sub.3 and l.sub.4 on the upper surface 10a of the work 10 is then derived. So as to allow arc start points A.sub.1 and A.sub.2 of the arc-shaped tracks c.sub.1 and c.sub.2 to correspond to arc end points B.sub.1 and B.sub.2 of the same on the upper and lower surfaces 10a and 10b of the work 10, the wire inclination angle is gradually varied during a machining operation along the first straight section 20 until the wire 1 simultaneously reaches the arc start points A.sub.1 and A.sub.2 of the arc-shaped tracks c.sub.1 and c.sub.2. Once the wire 1 has reached the arc start points A.sub.1 and A.sub.2, the arc-shaped section 21 is taper machined along the arc-shaped tracks c.sub.1 and c.sub.2 (each having the same radius) until the wire 1 simultaneously reaches the arc end points B.sub.1 and B.sub.2 of the arc-shaped tracks c.sub.1 and c.sub.2, while the wire inclination angle is held constant. Thereafter, the second straight section 22 is taper machined from the arc end points B.sub.1 and B.sub.2 while the inclination angle of the wire is gradually varied. Such taper machining causes the tracks derived from arc machining on the upper and lower surfaces 10a and 10b of the work 10 to have the same radius. Thus, a taper machining operation is performed at a constant speed on the upper and lower surfaces 10a and 10b of the work 10 without any variation in groove width. Consequently, taper machining with the same radius on the upper and lower surfaces of the work can be accomplished with a high degree of accuracy.
However, the method of taper machining to the same radius on the upper and lower surfaces of the work as disclosed in the prior invention is applicable only to a case where an arc-shaped section located between two straight sections is contoured tangential to both the straight sections (i.e., a case where two straight sections extend tangential to an arc). Thus, a machining operation can be performed only after positions where the straight sections reach the arc-shaped section as well as a radius of the arc-shaped section are determined.
In practice, however, a taper machining operation must be performed not only in a case as described above but also in a case of a convex circular contour or a concave circular contour, i.e., an arc-shaped contour having no tangential joint part, or in a contour having tangential joint parts but including two parallel straight sections with an arc-shaped section located therebetween for which machining should be accomplished in opposite directions. In such a case, with the conventional machining technique disclosed in the prior invention, joint parts between the straight sections and the arc-shaped section or a center point of the arc-shaped section cannot be definitely determined. For this reason, other complicated taper machining method must be employed for taper machining an arc-shaped section having the same radius on the upper and lower surfaces of a work but including no tangential joint part.